@inproceedings{5f28970a573a4efbb23b0d7749a97f74,
title = "Simultaneous Drawing of Layered Trees",
abstract = "We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to permute the vertices on the other layers (respecting the given tree embeddings) in order to minimize the number of crossings. While this problem is known to be NP-hard for multiple trees even on just two layers, we describe a dynamic program running in polynomial time for the restricted case of two trees. If there are more than two trees, we restrict the number of layers to three, which allows for a reduction to a shortest-path problem. This way, we achieve XP-time in the number of trees.",
keywords = "XP-algorithm, crossing-minimization, dynamic program, layered drawing, tree drawing",
author = "Julia Katheder and Kobourov, {Stephen G.} and Axel Kuckuk and Maximilian Pfister and Johannes Zink",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.; 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024 ; Conference date: 18-03-2024 Through 20-03-2024",
year = "2024",
doi = "10.1007/978-981-97-0566-5_5",
language = "English (US)",
isbn = "9789819705658",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "47--61",
editor = "Ryuhei Uehara and Katsuhisa Yamanaka and Hsu-Chun Yen",
booktitle = "WALCOM",
address = "Germany",
}